The invention relates to a method for encoding at least one hologram in a light modulation device, the encoding of which is carried out pixelwise, wherein the hologram is constructed from individual subholograms which are assigned to corresponding encoding regions in the light modulation device and which are respectively assigned to an object point of the object to be reconstructed with the hologram, wherein, with a virtual observer window, a defined viewing region is provided through which a reconstructed scene in a reconstruction space is observed by an observer, wherein a complex value of a wavefront for each individual object point is calculated in the virtual observer window and at least one value part of this complex value is corrected with a correction value and wherein the corrected complex values determined in this way for all object points are summed and transformed into the hologram plane of the light modulation device, in order to encode a hologram.
The invention furthermore relates to a method for encoding at least one hologram in a light modulation device, the encoding of which is carried out pixelwise, wherein the hologram is constructed from individual subholograms which are assigned to corresponding encoding regions in the light modulation device and which are respectively assigned to an object point of the object to be reconstructed with the hologram, wherein, with a virtual observer window, a defined viewing region is provided through which a reconstructed scene in a reconstruction space is observed by an observer, wherein each object point of the object to be reconstructed is holographically encoded in a subhologram, wherein amplitudes of the subholograms are corrected with a correction value and the subholograms corrected in this way are summed in the hologram plane, in order to encode a hologram.
As is known from prior documents of the Applicant, three-dimensional object data of the three-dimensional scene to be represented are written as a diffraction pattern of the scene to be reconstructed into encoding regions of a light modulation device. In this case, the calculation of the wavefront is carried out only for a small virtual observer window, which establishes a viewing region in an observer plane for an observer observing the reconstructed scene in a reconstruction space. The virtual observer window is in this case as large as or only minimally larger than the diameter or of the eye pupil of an eye of an observer. This, however, means that the virtual observer window may for example also be two or three times as large as the diameter of the eye pupil. It is therefore possible for the object points of the scene to be reconstructed to be encoded only in a small region of the light modulation device, defined by the respective object point, as so-called subholograms. In order to encode an object point in a subhologram, the complex light distribution of this object point or of an object section plane in the observer plane comprising the virtual observer window is calculated.
The light modulation device used may in this case be formed transmissively or reflectively, it having an arrangement of pixels as the modulation elements, which are separated from one another by intermediate spaces. In order to encode the pixels in amplitude and/or phase in the light modulation device, an electrode arrangement is provided, which is formed and arranged in the light modulation device in such a way that almost rectangular free spaces, which function as so-called pixels with a finite extent and constant amplitude transparency and/or phase transparency, are respectively formed between the electrodes. The pixels therefore have a defined pixel spacing from one another.
The almost rectangular configuration of the pixels is, however, disadvantageous to the extent that the complex wavefront in the predefined virtual observer window, and consequently also the reconstruction of the three-dimensional object in the reconstruction space between the virtual observer window and a hologram plane of the light modulation device, is vitiated by the effects of the finite pixel extent in the light modulation device. This means that, for example, undesired intensity changes may occur inside the virtual observer window. If the virtual observer window is larger than the eye pupil, then this effect is increasingly amplified. For example, the reconstructed three-dimensional scene may appear darker for a position of the eye pupil of an observer in the edge region or at the edge of the virtual observer window than for a position of the eye pupil of the observer in the middle of the virtual observer window. In other words, such a rectangular pixel aperture and pixel transparency has the effect that the intensity of the reconstructed three-dimensional scene, as perceived by the observer through the virtual observer window, may undesirably decrease from the middle of the virtual observer window toward its edge.
Solutions to this problem are known, for example, from DE 10 2006 042 467 A1 and DE 10 2008 000 589 A1 in the name of the Applicant. The way in which effects of the pixel transparency of a light modulation device on the intensity distribution in a virtual observer window of a holographic device can be corrected is described therein.
In DE 10 2006 042 467 A1 the correction is carried out in that, for a hologram calculation when applying Fourier transformation, the complex values of the object points or of the object section planes in a virtual observer window are modified by multiplying them by the reciprocal of the transform of the pixel shape and the pixel transparency, before the corrected complex values are summed and transformed into the hologram plane of the light modulation device.
For direct calculation of subholograms from object points, DE 10 2008 000 589 A1 describes that the correction of the pixel shape and of the pixel transparency is carried out in such a way that the amplitudes of the subholograms are multiplied by a suitably scaled reciprocal of the transform of the pixel shape and of the pixel transparency. The corrected subholograms are then summed to form a hologram.
For understanding of the calculation of subholograms or the encoding of holograms into the light modulation device, reference is made for example to WO2004/044659 A2, in which a device for the reconstruction of video holograms is described. FIG. 1 of the present application schematically represents such encoding, a three-dimensional object 1 being constructed from a plurality of object points, of which only four object points 1a, 1b, 1c and 1d are represented here in order to explain the encoding. A virtual observer window 2 is furthermore shown, through which an observer (indicated here by the eye represented) can observe a reconstructed scene. With the virtual observer window 2 as a defined viewing region and the four selected object points 1a, 1b, 1c and 1d, a pyramidal body is respectively projected through these object points 1a, 1b, 1c and 1d and in continuation onto a modulation surface 3 of the light modulation device (not represented in detail here). In the modulation surface 3, this results in encoding regions in the light modulation device which are assigned to the respective object points 1a, 1b, 1c and 1d of the object, in which the object points 1a, 1b, 1c and 1d are holographically encoded in a subhologram 3a, 3b, 3c and 3d. Each subhologram 3a, 3b, 3c and 3d is therefore written, or encoded, in only one region of the modulation surface 3 of the light modulation device. As can be seen from FIG. 1, depending on the position of the object points 1a, 1b, 1c and 1d, the individual subholograms 3a, 3b, 3c and 3d may overlap fully or only partially (i.e. only in certain regions) on the modulation surface 3. In order to encode, or write, a hologram for the object 1 to be reconstructed into the modulation surface 3 in this way, the procedure described above must be carried out with all object points of the object 1. The hologram is therefore constructed from a multiplicity of individual subholograms 3a, 3b, 3c, 3d, . . . 3n. The holograms computer-generated in this way in the light modulation device are illuminated for reconstruction by an illumination device (not represented here) in conjunction with an optical system.
Holograms for such a device for the reconstruction of holograms may, for example, be calculated by the method described in DE 10 2004 063 838 A1. DE 10 2004 063 838 A1 is intended to be fully incorporated here. It is, however, also possible that in the calculation of holograms, instead of the transformation of object section planes into the virtual observer window for the calculation there of a complex value distribution, according to DE 10 2004 063 838 A1, a complex value of a wavefront is respectively calculated for each individual object point of the object in the virtual observer window.
An alternative method for the calculation of holograms, which is likewise described by the Applicant, is based on an analytical calculation of subholograms in the modulation surface of the light modulation device in the form of lens functions.
With reference to FIG. 1, the individual subholograms 1a, 1b, 1c and 1d within the section of the hologram defined by the encoding regions have an essentially constant amplitude, the value of which is determined as a function of brightness and distance of the object points, and a phase which corresponds to a lens function, the focal length of the lens as well as the size of the encoding regions varying with the depth coordinate of the object point. Outside the section defined by the encoding regions, the amplitude of the individual subhologram has the value 0. The hologram is obtained by the complex-value sum of all subholograms 1a, 1b, 1c, 1d . . . 1n.
For the calculation of the hologram according to this alternative method, however, the complex value of a wavefront in the virtual observer window is not explicitly computationally determined. The method thus does not use a Fourier or Fresnel transformation. The calculation therefore has the advantage of substantially less computation time in comparison with the method described in document DE 10 2004 063 838 A1.
In a holographic device, besides the aforementioned pixel aperture of the light modulation device, there may for example be other optical components which can lead to a change in the intensity visible to the observer of a three-dimensional scene in the reconstruction space. Such components may, for example, be volume gratings (also referred to as volume holograms).
Volume gratings are diffraction gratings having a spatio-periodic variation in the absorption coefficient or the refractive index with arbitrary thickness. This means that volume gratings conventionally denote three-dimensional grating structures which are recorded in a medium that is thick in comparison with the wavelength of the illumination light. Glass may for example be used as the medium, although other materials may also be employed. Volume gratings offer the advantage that a plurality of gratings can be generated layerwise in a continuous medium.
Furthermore, volume gratings are generally distinguished by an angle selectivity, which means that the diffraction efficiency of a volume grating varies with the incidence angle of the incident light. Conventionally, this angle selectivity is generally used as an advantage. Under certain circumstances, however, too narrow an angle selectivity of the volume grating may also have perturbing influences on the holographic device for the reconstruction of three-dimensional scenes. When a volume grating is arranged in the beam path of a holographic device downstream of a light modulation device, too narrow an angle selectivity may, for example, lead to light which travels from a pixel of the light modulation device to a position at the edge of a virtual observer window in an observer plane being transmitted with a lesser efficiency by the volume grating than light which travels to the middle or center of the virtual observer window in the observer plane.